General relativistic razor-thin disks with magnetically polarized matter

Abstract

The origin of magnetic fields in the universe still remains unknown and constitutes one of the most intriguing questions in astronomy and astrophysics. Their significance is enormous since they have a strong influence on many astrophysical phenomena. In regards of this motivation, theoretical models of galactic disks with sources of magnetic field may contribute to understand the physics behind them. Inspired by this, we present a new family of analytical models for thin disks composed by magnetized material. The solutions are axially symmetric, conformastatic and are obtained by solving the Einstein-Maxwell Field Equations for continuum media without the test field approximation, and assuming that the sources are razor-thin disk of magnetically polarized matter. We find analytical expressions for the surface energy density, the pressure, the polarization vector, the electromagnetic fields, the mass and the rotational velocity for circular orbits, for two particular solutions. In each case, the energy-momentum tensor agrees with the energy conditions and also the convergence of the mass for all the solutions is proved. Since the solutions are well-behaved, they may be used to model astrophysical thin disks, and also may contribute as initial data in numerical simulations. In addition, the process to obtain the solutions is described in detail, which may be used as a guide to find solutions with magnetized material in General Relativity.

Self-gravitating razor-thin discs around black holes via multi-hole seeds

“…Interpreting z as a 'vertical' coordinate, we may apply a Kuzmin-like transformation [47] to the metric functions of the seed solution in order to obtain a razor-thin disc source, meaning a delta-like distributional source on the symmetry plane of the new system. This procedure is often called the 'displace, cut, and reflect' (DCR) method [17,20,22,25,48] and consists of making the transformation…”

Self-gravitating razor-thin disks around black holes via multihole seeds

“…Interpreting z as a "vertical" coordinate, we may apply a Kuzminlike transformation [43] to the metric functions of the seed solution in order to obtain a razor-thin disk source, meaning a delta-like distributional source on the symmetry plane of the new system. This procedure is often called the "displace, cut, and reflect" (DCR) method [18,20,21,24,44] and consists of making the transformation…”

“…disk. It is worth noting that, when we consider the covariant delta distribution δ, the formalism gives us, in a self-consistent manner, the "physical" (or "true") stress-energy tensor Q µ ν of the disk [21,22] without the need to differentiate between the "formal" and the "true" stress-energy tensors mentioned for instance in [14,15,18,20,21,26,35,44].…”